Calculus - Integration by Parts

Please help me solve this integration problem. I don't understand how to do it. Thank you!
∫e^(2x)*sin(2x)dx

  1. 👍 0
  2. 👎 0
  3. 👁 69
asked by Emma
  1. I do not believe you can do this in one integration-by-parts step. You must use the method twice.

    Let y = 2x and dx = dy/2, to simplify the problem to
    (1/2)∫e^y*sin(y)dy

    Next, let e^y = u and dv = siny dy
    du = e^y dy and v = -cos y

    (1/2)∫e^y*sin(y)dy = (1/2)*uv -(1/2)∫v*du
    = (1/2)[-u cos y +∫e^y cosy dy]

    Now you must apply integration by parts a second time on the
    +∫e^y cosy dy term

    This will give you an equation for
    ∫e^y*sin(y)dy that involves explicit functions of y.

    When you are all done, substitute 2x for y

    1. 👍 0
    2. 👎 0
    posted by drwls

Respond to this Question

First Name

Your Response

Similar Questions

  1. Stats: Joint Density Function

    Let the joint density function of X and Ybe given by: f(x)={kxy^2 for 0

    asked by Stephanie on October 18, 2006
  2. GENERAL CHEMISTRY

    CALCULATE THE pH AND HYDROLYSIS IN 0.10 M AlCl3 SOLUTION.Ka = 1.2 X 10-5 FOR [Al(OH2)6]+3,OFTEN ABBREVIATED Al+3.TELL WHETHER pH IS ACID OR BASE.GIVE IONIC EQUATION. Help us a little by telling us how much you know to do and

    asked by SHAWN on July 29, 2007
  3. Calculus

    The rate of performance is given by dN/dt=1/(2sqroot(t+1)) where N is the number of unity completed t hours after beginning a new tak. If 2 units are completed afer 3 hours, how many units are completed after 8 hours? N= INT 1/2

    asked by Chris on April 10, 2007
  4. College Math II

    Solve each problem. Find the quotient and remainder when x^2 – 5x + 9 is divided by x – 3. I don't understand how to divide and solve this problem. Can someone help me understand the steps on how to do it. Thanks.

    asked by Lori on November 21, 2009
  5. Pre calculus

    How do I solve this exponent problem? I understand the exponent rules, but I getting 1 but 1 is not the answer! I don't want anyone to solve the problem for me, I want to learn how to solve this type of problem. Thank you! Solve

    asked by anon on March 27, 2013
  6. Math

    Match the expressions with thier equivalent equations in the columns. List A: List B: 6x+12 6(1+x) 6+6x 6x-6 6(x-1) 6(x+2) Fill in the blank: The expression 6x+12 is equivalent to the expression __________ The expression 6+6x is

    asked by Nat on March 29, 2017
  7. Math

    I don't understand how to solve this problem: In solving the equation (x + 3)(x + 1) = 48, Eric stated that the solution would be x + 3 = 48 => x = 45or (x + 1) = 48 => x = 47 However, at least one of these solutions fails to work

    asked by Angelina on August 22, 2011
  8. Integral calculus

    Please can anyone help with the following problems - thanks. 1) Integrate X^4 e^x dx 2) Integrate Cos^5(x) dx 3) Integrate Cos^n(x) dx 4) Integrate e^(ax)Sinbx dx 5) Integrate 5xCos3x dx The standard way to solve most of these

    asked by Febby on April 13, 2007
  9. Math

    Hey! So, I've been working on this problem for awhile but I'm currently a bit dumbfounded on how to solve it. I think this question has been answered before but I still don't quite understand how it works or how to explain it. The

    asked by Z on June 20, 2016
  10. Algebra

    I don't understand how to do this problems: Solve for the variable r, C=2PIr (PI is the pi symbol thing then r is next to it) and this problem solve for the variable l, S=B+1/2Pl please help :) When you solve for a variable, you

    asked by Avalon on November 18, 2006

More Similar Questions